A canonical form for nonderogatory matrices under unitary similarity

A square matrix is nonderogatory if its Jordan blocks have distinct eigenvalues. We give canonical forms for (1) nonderogatory complex matrices up to unitary similarity, and (2) pairs of complex matrices up to similarity, in which one matrix has distinct eigenvalues. The types of these canonical forms are given by undirected and, respectively, directed graphs with no undirected cycles. (C) 2011 Elsevier Inc. All rights reserved.

A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs

Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.

Does Independent Component Analysis Play a Role in Unmixing Hyperspectral Data?

Chapter in Book Proceedings with Peer Review First Iberian Conference, IbPRIA 2003, Puerto de Andratx, Mallorca, Spain, JUne 4-6, 2003. Proceedings

Estimation and hypothesis testing in mixed linear models

Dissertação apresentada para obtenção do Grau de Doutor em Matemática, Estatística, pela Universidade Nova de Lisboa, faculdade de Ciências e Tecnologia

Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

Feedback design for regularizing descriptor systems

This paper surveys numerical techniques for the regularization of descriptor (generalized state-space) systems by proportional and derivative feedback. We review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the Weierstraß canonical form. Three condensed forms display the controllability and observability properties of a descriptor system. The condensed forms are obtained through orthogonal equivalence transformations and rank decisions, so they may be computed by numerically stable algorithms. In addition, the condensed forms display whether a descriptor system is regularizable, i.e., when the system pencil can be made to be regular by derivative and/or proportional output feedback, and, if so, what index can be achieved. Also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Função quadrática

In general, the study of quadratic functions is based on an excessive amount formulas, all content is approached without justification. Here is the quadratic function and its properties from problems involving quadratic equations and the technique of completing the square. Based on the definitions we will show that the graph of the quadratic function is the parabola and finished our studies finding that several properties of the function can be read from the simple observation of your chart. Thus, we built the whole matter justifying each step, abandoning the use of decorated formulas and valuing the reasoning

Complexation of some trivalent lanthanides, scandium(III) and thorium(IV) by benzylidenepyruvates in aqueous solution

The protonation constants of 4-methylbenzylidenepyruvate (4Me-BP) and 4-isopropylbenzylidenepyruvate (4IP-BP) as well as the stability constants of their binary 1:1 complexes with Cu(II), La(III), Pr(III), Sm(III), Eu(III), Yb(III), Sc(III) and Th(IV) have been determined spectrophotometrically in aqueous solution at 25°C and ionic strength 0.500 M, maintained with sodium perchlorate. For all metal ions considered, the stability changes move in the same direction as the pKa of the ligands. Linear free energy relationships, as applied to oxygen donor substances, suggest the -COCOO- moiety as the metal binding site of the ligands. The results are discussed mainly taking into account that benzylidenepyruvates, besides the α-keto canonical form, may display other forms in aqueous solution with changing pH and the possible occurrence of extra intra-ligand charge polarization, induced by metal ions.

Global optimization for the ℋ∞-norm model reduction problem

A branch and bound algorithm is proposed to solve the [image omitted]-norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The [image omitted]-norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.

Estabilizador de sistemas de potência digital aplicado a uma unidade geradora da UHE de Tucuruí

Este trabalho apresenta o desenvolvimento e resultados de testes de campo de um estabilizador de sistemas de potência (ESP) digital, destinado ao amortecimento de oscilações eletromecânicas em sistemas interligados. Os testes experimentais foram efetuados em uma das unidades hidrogeradoras, de 350 MVA, da UHE de Tucuruí. A lei de controle amortecedor do ESP digital foi embarcada em um sistema de hardware baseado em um controlador digital de sinais (DSPIC 30f5011). A estrutura da lei de controle é na forma canónica RST, de tempo discreto, sendo os parâmetros do controlador calculados através da técnica de deslocamento radial de pólos. Para fins de projeto, a dinâmica da planta, no ponto de operação considerado, foi representada por um modelo paramétrico, o qual foi estimado a partir de dados medidos em campo. Os resultados experimentais mostraram um excelente desempenho do ESP digital no amortecimento de um dos modos eletromecânicos observável na UHE de Tucuruí.

Gráfico interactivo de las relaciones derivativas entre palabras del español

[ES] La aplicación Gráfico interactivo de las relaciones derivativas entre palabras del español se centra en realizar un tratamiento a la información recabada en la tesis Sistema computacional de la gestión morfológica del español, de toda la información que contiene esta tesis este proyecto hace uso recogiendo cualquier palabra introducida por el usuario, buscando su forma canónica y devolviendo en forma gráfica la familia de palabras relacionada con esta, mediante un grafo. Esta aplicación web tiene como objetivo hacer amena la legibilidad y consulta de la información mencionada. Para lograr este objetivo se ha desarrollado una interfaz muy sencilla para el usuario, en la que éste solo tiene que introducir una palabra y relacionarla mediante un click. Una vez realizada la búsqueda, la aplicación permite al usuario interactuar con el grafo, pudiendo moverlo por la pantalla a su antojo, también tiene la función de mostrar los hijos de un nodo hoja al pasar el puntero por encima de éste y al hacer doble click sobre un nodo hoja, sea hijo o nieto de la raíz, devolviendo un nuevo grafo con el nodo seleccionado como raíz del mismo y mostrando sus hijos y nietos si los tuviera.

Controlling systems with a single actuator

In this paper the problem of designing a single actuator control for a class of systems is addressed. The existence of such control is studied and several ways for designing such control are provided. The results depend either on the rational canonical form or on the Jordan structure associated with the matrix which characterizes the system dynamics. The constructed control laws can be employed in the design of minimum cost controllers for a large variety of systems.

Gender, language and floor apportionment in political debates

Political debates are speech events which foreground issues of power and the `floor', and allow the opportunity of assessing the ways in which the gender of participants affects their construction as more or less powerful participants in debates. Debates in the British House of Commons are adversarial in style, making it appropriate to view the floor as `the site of a contest where there is a winner and a loser'. Previous research into political debates has found that male participants violate the formal rules in debates more than their female counterparts, in order to gain the floor. Although the canonical form and rules of debates exist to `permit the equalization of turns', rule violations are common, and inequalities between participants exist. In this article legal and illegal interventions are evaluated in five debates in order to establish the extent to which the gender of participants is related to the control that an individual has over the debate floor.